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Research demonstrates the presence of cycle subdivisions in high chromatic digraphs, implying structural insights into directed graphs.
Let C be an oriented cycle with two blocks and let n denote the number of its vertices. We show that every (n+2)-chromatic digraph spanned by a Hamiltonian directed path contains a subdivision of C. This bound is tight.
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Ghazal et al. (2026) studied this question.
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